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Display information for equation id:math.1255.159 on revision:1255

* Page found: Das d'Alembertsche Prinzip (eq math.1255.159)

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Normalschwingungen Eq: math.1515.20

Hash: 529a8a7debd9b79249f530da06bffc90

TeX (original user input):

\begin{align}
  & \sum\limits_{k}{({{V}_{lk}}-{{\omega }^{2}}{{T}_{lk}}){{A}_{k}}=0}\left| \cdot \sum\limits_{l}{{{A}_{l}}^{*}} \right. \\
 & \sum\limits_{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}-}{{\omega }^{2}}\sum\limits_{l,k}{{{T}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}=0 \\
 & {{\omega }^{2}}=\frac{\sum\limits_{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}}{\sum\limits_{l,k}{{{T}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}} \\
 & \sum\limits_{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}=\frac{1}{2}\sum\limits_{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}+\frac{1}{2}\sum\limits_{l,k}{{{V}_{kl}}{{A}_{k}}^{*}{{A}_{l}}=}\frac{1}{2}\sum\limits_{l,k}{{{V}_{lk}}\left( {{A}_{l}}^{*}{{A}_{k}}+{{A}_{k}}^{*}{{A}_{l}} \right)=}\frac{1}{2}\sum\limits_{l,k}{{{V}_{lk}}2\cdot \operatorname{Re}\left( {{A}_{l}}^{*}{{A}_{k}} \right)} \\
\end{align}

TeX (checked):

{\begin{aligned}&\sum \limits _{k}{({{V}_{lk}}-{{\omega }^{2}}{{T}_{lk}}){{A}_{k}}=0}\left|\cdot \sum \limits _{l}{{{A}_{l}}^{*}}\right.\\&\sum \limits _{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}-}{{\omega }^{2}}\sum \limits _{l,k}{{{T}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}=0\\&{{\omega }^{2}}={\frac {\sum \limits _{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}}{\sum \limits _{l,k}{{{T}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}}}\\&\sum \limits _{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}={\frac {1}{2}}\sum \limits _{l,k}{{{V}_{lk}}{{A}_{l}}^{*}{{A}_{k}}}+{\frac {1}{2}}\sum \limits _{l,k}{{{V}_{kl}}{{A}_{k}}^{*}{{A}_{l}}=}{\frac {1}{2}}\sum \limits _{l,k}{{{V}_{lk}}\left({{A}_{l}}^{*}{{A}_{k}}+{{A}_{k}}^{*}{{A}_{l}}\right)=}{\frac {1}{2}}\sum \limits _{l,k}{{{V}_{lk}}2\cdot \operatorname {Re} \left({{A}_{l}}^{*}{{A}_{k}}\right)}\\\end{aligned}}

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\begin{aligned} \sum_{k} (V_{l k} - ω^{2} T_{l k}) A_{k} = 0 | \cdot \sum_{l} {A_{l}}^{*} \\ \sum_{l, k} V_{l k} {A_{l}}^{*} A_{k} - ω^{2} \sum_{l, k} T_{l k} {A_{l}}^{*} A_{k} = 0 \\ ω^{2} = \frac{\sum_{l, k} V_{l k} {A_{l}}^{*} A_{k}}{\sum_{l, k} T_{l k} {A_{l}}^{*} A_{k}} \\ \sum_{l, k} V_{l k} {A_{l}}^{*} A_{k} = \frac{1}{2} \sum_{l, k} V_{l k} {A_{l}}^{*} A_{k} + \frac{1}{2} \sum_{l, k} V_{k l} {A_{k}}^{*} A_{l} = \frac{1}{2} \sum_{l, k} V_{l k} ({A_{l}}^{*} A_{k} + {A_{k}}^{*} A_{l}) = \frac{1}{2} \sum_{l, k} V_{l k} 2 \cdot ℜ ({A_{l}}^{*} A_{k}) \end{aligned}

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Identifiers

$k$

$V_{l k}$

$ω$

$T_{l k}$

$A_{k}$

$l$

$A_{l}$

$l$

$k$

$V_{l k}$

$A_{l}$

$A_{k}$

$ω$

$l$

$k$

$T_{l k}$

$A_{l}$

$A_{k}$

$ω$

$l$

$k$

$V_{l k}$

$A_{l}$

$A_{k}$

$l$

$k$

$T_{l k}$

$A_{l}$

$A_{k}$

$l$

$k$

$V_{l k}$

$A_{l}$

$A_{k}$

$l$

$k$

$V_{l k}$

$A_{l}$

$A_{k}$

$l$

$k$

$V_{k l}$

$A_{k}$

$A_{l}$

$l$

$k$

$V_{l k}$

$A_{l}$

$A_{k}$

$A_{k}$

$A_{l}$

$l$

$k$

$V_{l k}$

$A_{l}$

$A_{k}$

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